Developing and deploying a use-inspired metapopulation framework for stratified health outcomes

People involved

Roadmap

Motivation

• Public health decision makers increasingly rely on epidemiological models to:
  • Forecast likely futures
  • Stress-test interventions
  • Plan resource allocation (e.g., beds, staffing)
• Our team at Argonne (led by Chick Macal and Jonathan Ozik) was one of the four modeling groups in the Illinois Governor’s COVID-19 Modeling Taskforce, providing critical insights to support decision making during the pandemic
  • We produced scenario analyses (e.g., potential impacts of mitigation efforts) and projections (e.g., future hospital capacity issues).
  • Meetings were held twice weekly and analyses provided to the IDPH, CDPH, and Governor’s office weekly
  • Primary concerns became:
    1. developing analyses that were of utility to stakeholders
    2. fast time-to-solution

Motivation

Motivation

MetaRVM - Disease model

MetaRVM - Population mixing

• Allows for subpopulations based on demographic characteristics, e.g., based on age: children (green boxes), working-age adults (blue boxes), and seniors (orange boxes)
• Allows for different mixing patterns for daytime and nighttime: obtained through social mixing studies or through synthetic population schedules

Mixing and force of infection

• For each stratum, the force of infection depends on:
  • Mixing rates between the stratum \(i\) and \(j\) \(M = (m_{ij}), \quad, i, j \in \mathcal{J}\) (set of all strata)
  • Prevalence of infectious individuals in \(j\)th stratum at time \(t\), \(I_t^{(j)}\), where \(j \in \mathcal{J}\)

Mixing and force of infection

• Effective interacting population (exclude Hospitalized [H], Dead [D] from total Population [P])

\[ \mathrm{MP}_t^{(j)} = P_t^{(j)} - H_t^{(j)} - D_t^{(j)}, \qquad j \in \mathcal{J}. \]

• Mixing across demographic strata

\(M\): mixing matrix \[ M = (m_{ij}), \qquad \sum_{j \in \mathcal{J}} m_{ij} = 1 \ \forall i, \]

\[ \mathrm{MP}_{t,\text{eff}}^{(j)} = \sum_{i \in \mathcal{J}} m_{ij}\,\mathrm{MP}_t^{(i)}, \quad S_{t,\text{eff}}^{(j)} = \sum_{i \in \mathcal{J}} m_{ij}\,S_t^{(i)}, \quad I_{t,\text{eff}}^{(j)} = \sum_{i \in \mathcal{J}} m_{ij}\,I_t^{(i)}. \]

Mixing and force of infection

• Force of infection (Susceptible [S] vs Vaccinated [V])

\[ \lambda_{s,t}^{(j)} = \beta_s \frac{I_{t,\text{eff}}^{(j)}}{\mathrm{MP}_{t,\text{eff}}^{(j)}}, \qquad \lambda_{v,t}^{(j)} = \beta_v \frac{I_{t,\text{eff}}^{(j)}}{\mathrm{MP}_{t,\text{eff}}^{(j)}}. \]

• Susceptible [S] → Exposed [E] transition in stratum (j)

Age-stratified model – Illustration

Ingredients

Age-stratified model – Illustration

Age-stratified model – Illustration

Daytime vs Nightime mixing

MetaRVM in action

Prepare configuration

run_id: age-stratified
population_data:
  mapping: demographic_mapping.csv
  initialization: population_init.csv
  vaccination: vaccination.csv
mixing_matrix:
  weekday_day: m_wd_d.csv
  weekday_night: m_wd_n.csv
  weekend_day: m_we_d.csv
  weekend_night: m_we_n.csv
disease_params:
  ts: 0.5
  tv: 0.3
  ve : 0.5
  dv: 158
  dp: 1
  de: 3
  da: 5
  ds: 6
  dh: 4
  dr: 187
  pea: 0.333
  psr: 0.95
  phr: 0.97
sub_disease_params:
    age:
      0-17:
        ts: 0.5
        tv: 0.1
        pea: 0.1
        psr: 0.99
      18-64:
        ts: 0.5
        tv: 4
        pea: 0.1
        psr: 0.99
      65+:
        ts: 0.5
        tv: 7
        pea: 0.3
        psr: 0.97
simulation_config:
  start_date: 8/01/2023 # m/d/Y
  length: 365

MetaRVM in action

Run simulation

library(MetaRVM)
options(odin.verbose = FALSE)
out <- metaRVM("R/config.yaml")
print(out)

MetaRVM Results Object
=====================
Instances: 1 
Populations: 3 
Date range: 2023-08-01 to 2024-07-30 
Total observations: 33945 
Disease states: D, E, H, I_all, I_asymp, I_eff, I_presymp, I_symp, P, R, S, V, cum_V, mob_pop, n_EI, n_EIpresymp, n_HD, n_HR, n_HRD, n_IasympR, n_IsympH, n_IsympR, n_IsympRH, n_SE, n_SV, n_VE, n_VS, n_preIsymp, p_HRD, p_SE, p_VE 

MetaRVM in action

Run simulation

library(MetaRVM)
options(odin.verbose = FALSE)
out <- metaRVM("R/config.yaml")
print(out)

MetaRVM Results Object
=====================
Instances: 1 
Populations: 3 
Date range: 2023-08-01 to 2024-07-30 
Total observations: 33945 
Disease states: D, E, H, I_all, I_asymp, I_eff, I_presymp, I_symp, P, R, S, V, cum_V, mob_pop, n_EI, n_EIpresymp, n_HD, n_HR, n_HRD, n_IasympR, n_IsympH, n_IsympR, n_IsympRH, n_SE, n_SV, n_VE, n_VS, n_preIsymp, p_HRD, p_SE, p_VE 

out$results

             date    age   race   zone disease_state        value instance
           <Date> <char> <char> <char>        <char>        <num>    <int>
    1: 2023-08-01   0-17    all    all             D 2.191379e-05        1
    2: 2023-08-01   0-17    all    all             E 2.434292e-01        1
    3: 2023-08-01   0-17    all    all             H 1.344297e-02        1
    4: 2023-08-01   0-17    all    all         I_all 7.420794e-01        1
    5: 2023-08-01   0-17    all    all       I_asymp 2.299324e-02        1
   ---                                                                    
33941: 2024-07-30    65+    all    all          n_VS 5.717389e+01        1
33942: 2024-07-30    65+    all    all    n_preIsymp 2.301472e+01        1
33943: 2024-07-30    65+    all    all         p_HRD 9.516258e-02        1
33944: 2024-07-30    65+    all    all          p_SE 9.283081e-04        1
33945: 2024-07-30    65+    all    all          p_VE 3.714267e-04        1

MetaRVM in action

Visualize

# extract new hospitalizations
out_H <- out$subset_data(disease_states = "n_IsympH")

library(ggplot2)
ggplot(out_H$results, aes(x = date, y = value, color = age)) + 
  geom_line() + 
  ylab("new hospitalizations") + theme_bw()

MetaRVM in action

Use of checkpoints

simulation_config:
  start_date: 8/01/2023 # m/d/Y
  length: 60
  checkpoint_dir: "path-to-the-checkpoint-directory"
  restore_from: "path-to-checkpoint-file"

Run a simulation and checkpoint

out <- metaRVM(checkpoint_config)
print(out)

MetaRVM Results Object
=====================
Instances: 1 
Populations: 3 
Date range: 2023-08-01 to 2024-01-27 
Total observations: 16740 
Disease states: D, E, H, I_all, I_asymp, I_eff, I_presymp, I_symp, P, R, S, V, cum_V, mob_pop, n_EI, n_EIpresymp, n_HD, n_HR, n_HRD, n_IasympR, n_IsympH, n_IsympR, n_IsympRH, n_SE, n_SV, n_VE, n_VS, n_preIsymp, p_HRD, p_SE, p_VE 

# Check what checkpoint files were created
checkpoint_files <- list.files(checkpoint_dir, 
                               pattern = "^chk_.*\\.Rda$",
                               full.names = FALSE)
checkpoint_files

[1] "chk_2024-01-27_1.Rda"

MetaRVM in action

Use of checkpoints

simulation_config:
  start_date: 8/01/2023 # m/d/Y
  length: 60
  checkpoint_dir: "path-to-the-checkpoint-directory"
  restore_from: "path-to-checkpoint-file"

Restore from a checkpoint

out <- metaRVM(config_resume)
print(out)

MetaRVM Results Object
=====================
Instances: 1 
Populations: 3 
Date range: 2024-01-28 to 2024-07-25 
Total observations: 16740 
Disease states: D, E, H, I_all, I_asymp, I_eff, I_presymp, I_symp, P, R, S, V, cum_V, mob_pop, n_EI, n_EIpresymp, n_HD, n_HR, n_HRD, n_IasympR, n_IsympH, n_IsympR, n_IsympRH, n_SE, n_SV, n_VE, n_VS, n_preIsymp, p_HRD, p_SE, p_VE 

MetaRVM in action

Use of checkpoints

MetaRVM in action

Use of checkpoints

Tracking age-stratified influenza hospitalizations in Chicago

• Goal:
  • Calibrate MetaRVM to weekly hospitalizations
  • Parameters to estimate:
    • \(ts\): transmissibility for susceptible population
    • \(tv\): transmissibility for vaccinated population
    • \(pea\): proportion of asymptomatic cases
    • \(psh\): proportion of hospitalized among symptomatic cases

Tracking age-stratified influenza hospitalizations in Chicago

• Approach:
  • Apply Bayesian Optimization to find relevant trajectories matching the observed data (Fadikar et al. (2023))

Tracking age-stratified influenza hospitalizations

Figure shows age-stratified hospitalization trajectories for the 2023–24 season that align with observed hospitalization counts (in black dots). Blue bands show the model-generated trajectories, and vertical dashed lines indicate the calibration windows where checkpoints are induced.

Tracking age-stratified influenza hospitalizations

Week 1 - 10

Week 11 - 20

Week 21 - 30

Figure shows the time-varying estimates of the transmission parameters (\(ts\)) for each age group, and for each 10-week calibration period. Diagonal panels display marginal posterior distributions for each age group, and off-diagonal panels show joint posterior contours.

Closing thoughts

• Enables tracking stratified health outcomes.
• Flexible in defining strata, time-strata varying model parameters.
• Available as an R-package.